Updated Math & Fractions

Fraction Calculator

Add, subtract, multiply, divide, simplify, convert fractions, and solve fraction equations with automatic step-by-step solutions.

Fraction Operations Simplify & Convert Mixed Numbers Equation Solver

All-in-One Fraction Calculator

Use tabs to switch between basic operations, simplification, conversion, mixed numbers, decimals and percents, equation solving, and a fraction toolkit.

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Use this toolkit to support fraction work: simplify fractions, find common denominators, and understand how numbers factor.

Fraction Calculator – Add, Subtract, Multiply, Divide, Simplify, Convert & Solve

Fractions appear everywhere — from school math to cooking, construction, engineering, finance, statistics, and real-world problem-solving. This all-in-one Fraction Calculator helps you handle every type of fraction task: performing basic operations, simplifying to lowest terms, converting between formats, working with mixed numbers, and solving equations step by step.

Whether you are a student, a teacher, a parent helping with homework, or someone who frequently works with ratios and parts of a whole, this calculator gives you fast results with clear explanations. Every output includes fraction form, mixed numbers, decimal equivalents, percent values, and (when applicable) step-by-step solutions.

Understanding Fractions

A fraction represents a part of a whole. It consists of two numbers:

Fraction = numerator ÷ denominator = n/d

The numerator tells how many parts you have, and the denominator shows how many equal parts the whole is divided into. Fractions are useful because they express values that are not whole numbers and can show ratios or proportions.

For example:

  • 1/2 means one part out of two equal parts
  • 3/4 means three parts out of four
  • 7/3 is an improper fraction where the numerator is larger than the denominator
  • 2 1/5 is a mixed number combining a whole number and a fraction

Types of Fractions

Fractions come in different forms depending on their structure:

  • Proper fraction: numerator < denominator (example: 3/5)
  • Improper fraction: numerator ≥ denominator (example: 9/4)
  • Mixed number: whole + fraction (example: 2 3/7)
  • Equivalent fraction: fractions that look different but are equal (example: 1/2 = 2/4 = 3/6)

1. Adding and Subtracting Fractions

Addition and subtraction require a common denominator. This calculator automatically finds the least common denominator (LCD), adjusts the numerators, and simplifies the final result.

a/b + c/d = (ad + bc) / bd
a/b − c/d = (ad − bc) / bd

Example:

1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2

2. Multiplying Fractions

Multiplication is straightforward — multiply the numerators together and the denominators together.

(a/b) × (c/d) = (ac)/(bd)

Before finalizing the result, the calculator automatically simplifies the fraction.

3. Dividing Fractions

Dividing fractions uses the reciprocal method — multiply the first fraction by the flipped version of the second.

(a/b) ÷ (c/d) = (a/b) × (d/c)

4. Simplifying Fractions

Simplification reduces a fraction to its lowest terms. It works by dividing the numerator and denominator by their greatest common divisor (GCD).

Simplest form = (n ÷ GCD) / (d ÷ GCD)

Example:

12/20 → GCD = 4 → 12 ÷ 4 = 3, 20 ÷ 4 = 5 → simplified = 3/5

5. Converting Fractions, Decimals, and Percents

Conversions help compare values or fit formats required in exams, formulas, or real-world tasks.

  • Fraction → Decimal: divide numerator by denominator
  • Decimal → Fraction: rewrite as fraction and simplify
  • Fraction → Percent: multiply decimal form by 100
  • Percent → Fraction: write % as number/100 and simplify

6. Working with Mixed and Improper Fractions

Mixed numbers convert to improper fractions using:

Improper = (whole × denominator + numerator) / denominator

Improper fractions convert back by dividing numerator by denominator:

whole = floor(n ÷ d), remainder = n mod d

7. Fraction Equation Solver

The calculator solves proportion equations and “fraction of a number” problems automatically.

a/b = c/d → cross multiply: ad = bc

This helps with school algebra, chemistry ratios, finance comparisons, and scaling recipes or blueprints.

8. Fraction Toolkit (GCD, LCM, LCD)

The toolkit helps with:

  • GCD — greatest common divisor used for simplification
  • LCM — least common multiple used for common denominators
  • LCD — least common denominator for adding/subtracting fractions
  • Prime factorization — useful for understanding fraction structure

Why Fractions Matter

Fractions are used everywhere:

  • Cooking: 1/3 cup, 1/2 teaspoon, recipe scaling
  • Construction: measurement conversions, ratios
  • Finance: interest rates, ratios, discounted prices
  • Data analysis: probabilities, statistics
  • Education: math learning from grade school to university
  • Science: chemical ratios, concentration formulas

Understanding fractions helps you solve problems more accurately and efficiently — especially when decimals or whole numbers are not precise enough.

Real-World Examples Using the Fraction Calculator

Example 1: Scaling a Recipe

A recipe requires 3/4 cup of sugar. You want to make half the recipe.

(3/4) × (1/2) = 3/8 cup

Example 2: Construction Measurement

You have a board that is 7 3/8 inches and need to remove 1 1/4 inches.

7 3/8 = 59/8
1 1/4 = 5/4 = 10/8
59/8 − 10/8 = 49/8 = 6 1/8

Example 3: Converting a Decimal to a Fraction

Convert 0.375 to a fraction:

0.375 = 375/1000 → simplified = 3/8

Example 4: Solving a Proportion

Given:

a/4 = 6/8
Cross multiply → 8a = 24 → a = 3

Study Tips for Mastering Fractions

  • Always simplify your final answer — exams expect lowest terms
  • Convert mixed numbers to improper fractions before multiplying/dividing
  • Use LCD for faster addition/subtraction
  • Remember: dividing fractions means multiply by the reciprocal
  • Decimals with limited digits are often easier to convert using powers of 10

Using This Calculator for Learning

Each tab includes step-by-step solutions, which makes this a powerful learning tool for students and tutors. You can follow each operation in detail, which helps build strong fraction intuition and problem-solving confidence.

Using This Calculator for Work

Professionals in construction, engineering, architecture, finance, statistics, science, and culinary arts use fractions daily. This calculator is especially helpful when precision matters, or when working quickly under deadlines.

Frequently Used Fraction Formulas

Addition: a/b + c/d = (ad + bc) / bd

Subtraction: a/b − c/d = (ad − bc) / bd

Multiplication: (a/b)(c/d) = ac/bd

Division: (a/b) ÷ (c/d) = ad/bc

Mixed → Improper: W n/d = (Wd + n)/d

Percent → Fraction = p/100

Fraction → Decimal = n ÷ d

More Tools to Explore

MyTimeCalculator includes dozens of math tools — from percentage calculators to GCF/LCM solvers, scientific calculators, mixed number converters, and equation calculators. Combine this Fraction Calculator with those tools for deeper learning or more advanced problem solving.

Fraction Calculator – Frequently Asked Questions
To add fractions, find a common denominator (preferably the least common denominator), adjust the numerators, add them, and simplify. The Fraction Calculator does this instantly for you.
Divide the numerator and denominator by their greatest common divisor (GCD). For example: 18/24 → divide both by 6 → 3/4.
Write the decimal over a power of 10, then simplify. Example: 0.25 = 25/100 = 1/4. The calculator does this automatically.
Yes. Convert each mixed number to an improper fraction, multiply normally, then convert back to a mixed number if needed.
Dividing by a fraction is multiplying by its reciprocal. Example: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8.
LCD is the least common multiple applied specifically to denominators. LCM works for all whole numbers. For fractions, LCD = LCM of denominators.
Cross multiply: if ad = bc, the fractions a/b and c/d are equivalent. The calculator verifies this automatically during operations.
Yes. On the "Equation Solver" tab, every step is shown — including cross multiplication, simplification, and final reduction.